Classification of Acids and Acidities in Ih Ice - The Journal of Physical

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J. Phys. Chem. C 2009, 113, 7342–7354

Classification of Acids and Acidities in Ih Ice Anna Uritski, Itay Presiado, Yuval Erez, Rinat Gepshtein, and Dan Huppert* Raymond and BeVerly Sackler Faculty of Exact Sciences, School of Chemistry, Tel AViV UniVersity, Tel AViV 69978, Israel ReceiVed: January 13, 2009; ReVised Manuscript ReceiVed: February 25, 2009

The proton concentration in methanol-doped ice samples was monitored by measuring the fluorescence quenching process of 1-naphthol-4-sulfonate (1N4S) by employing a time-resolved emission technique. We used both weak and strong acids in order to introduce protons into Ih ice. We found that for a certain concentration of acid the quenching rate strongly depended on the kind of acid used. In strong acid samples the quenching rate was much larger than for weak acids. Our qualitative explanation of the results is that the acidity scale of commonly used acids in aqueous solutions is also applicable for Ih ice. We found that, among the group of weak acids studied, HF is a relatively stronger acid. This finding is in accord with previous electrical conductance measurements. Introduction The physics of ice,1-4 which has been studied for a long time, poses many questions that even today are left unanswered.2 Recently ice regained its popularity in earth science due to environmental ramifications such as in ionization of hydrochloric acid on stratospheric ice particles as a key step in the depletion of the stratospheric ozone.5 Lattice imperfections give rise to electrical conduction, diffusion and relaxation phenomena. Ice exhibits a high static relative permittivity which is on par with that of liquid water. There are two types of structural defects that are largely responsible for the ice’s electrical properties: (1) Ion defects, which are the result of proton motion from one end of the bond to the other, thus creating a H3O+, OH- ion pair.6 Conduction is then carried out by means of successive proton jumps (the von Grotthuss mechanism). (2) Bjerrum defects,7 which are orientational defects caused by the rotation of a water molecule to produce either a doubly protonated bond (D-defect) or a deprotonated bond (L-defect). Over the years ice has challenged the best electrical equipment. Nowadays, quantum-mechanical ab initio calculations and dynamical simulations present an efficient way to study the mechanism of proton transfer and mobility in ice. Ohmine and co-workers8 employed QM/MM methods to study the mechanism of the excess proton transfer in ice, and proposed that in ice the excess proton is localized in an L-defect. Podeszwa and Buch9 studied the structure and dynamics of orientational defects in ice by molecular dynamics simulations. Their findings suggest that the defect structure is quite different from the one originally proposed by Bjerrum.7 For the L-defect, one water molecule is displaced by ∼1 Å from the crystal lattice site. Defect jumps occur via vibrational phase coincidence. In the early 1960s it was estimated from the electrical conductivity measurements of Eigen10,11 that the proton mobility in ice is 10-100 times larger than in water. In numerous further measurements it was found that at about 263 K the proton mobility in ice (0.8 × 10-4 cm2 V-1 s-1) is smaller than in water12 by about a factor of 2 (when compared to supercooled * *Corresponding author. E-mail: [email protected]. Telephone: 972-3-6407012. Fax: 972-3-6407491.

liquid water13,14 at the same temperature). The large proton conductivity of ice found in Eigen’s experiments was explained as arising from large surface conductivity rather than from the bulk conductivity.3 In the 1973 ice conference in Ottawa, Onsager, Engelhardt and others gave up on the idea of ice as an intrinsic protonic semiconductor.15 For over 30 years16-25 excited-state intermolecular proton transfer (ESPT) to a solvent or to a base in a solution has been widely researched in the liquid phase. In some of our previous works26 we reported on the proton diffusion constant in ice Ih. For that purpose we used the photoprotolytic cycle of the photoacid 2-naphthol-6,8-disulfonate (2N68DS) in liquid water and in ice in the presence of small concentrations of a strong mineral acid, HCl. We deduced the proton diffusion constant in ice from the experimental data fit. We found that the proton diffusion in ice Ih at 240-263 K is about 10 times larger than in liquid water at 295 K. In a subsequent work we studied the fluorescence quenching of flavin mononucleotide (FMN) in liquid water and in ice in the presence of small concentrations of the strong mineral HCl acid.27 We continued our study with the same methods28 using 1-naphthol derivatives, 1-naphthol4-sulfonate (1N4S) and 1-naphthol-3sulfontate (1N3S) in ice. The deprotonated form of 1-naphthol derivatives, RO-*, reacts with an excess proton in solution to reform the ground-state protonated form, ROH. For the photoreactive compounds, FMN, 1N4S and 1N3S we deduced the proton diffusion constant in ice from the fit of the experimental time-resolved emission data by using the irreversible diffusion-assisted recombination model based on the Debye-Smoluchowski equation. The conclusions that were drawn were the same as in our first work, namely, that the proton diffusion constant is 10 times larger than in water. Already in 1983 Nagle29 advocated the existence of proton wires in ice and in enzymatic systems in which the proton transport is carried out via a concerted mechanism (von Grotthuss mechanism) on a limited length scale. The defect concentration created in pure ice by deviating from an ideal ice structure is relatively small. It can be influenced by introducing dopant molecules into the lattice. In the past, in order to learn about the electrical properties of ice, extrinsic defects were generated by doping the ice with HF. It was assumed that HF and NH3 were of particular interest since it

10.1021/jp900338c CCC: $40.75  2009 American Chemical Society Published on Web 04/03/2009

Classification of Acids and Acidities in Ih Ice was believed that these molecules substituted H2O molecules with a minimum ice-lattice deformation.30 The disappearance of the configurational susceptibility at the crossover, which is a consequence of Jaccard’s theory,6 was first observed by Steinemann31 on ice doped with different amounts of HF and is considered as one of the most impressive arguments in favor of the complementary action of the Bjerrum and ion defects in the ice lattice. Subsequently, the HF-doped ice was studied by Camplin and Glen13 and by Runck et al.32 Several physical properties of dilute HF solutions in water appear to be quite unusual. For instance, the ionic dissociation equilibrium constant, Ka, of HF is much smaller than that of other hydrogen halides. As a result, understanding the interaction of acid molecules with water molecules in ice has received considerable attention, and so has the extent of ionic dissociation of HF in ice33 and at its surface.34 At present, there are numerous studies regarding hydrochloric acid (HCl) dissociation on the ice surface,5 since ionization of HCl on stratospheric ice particles is believed to be a key step in the depletion of stratospheric ozone. Hynes and co-workers performed molecular dynamics simulation to study HCl ionization on crystalline pure water ice surface.35 Recent molecular dynamics simulations indicate that molecular HCl can penetrate into the ice lattice, which may lead to the encapsulation of this molecule in the lattice structure.36 In the current study we set a goal to qualitatively classify the acidity of acids in ice Ih. For our current experiments we used the fluorescence quenching of the RO-* form of 1-naphthol4-sulfonate (1N4S) by protons. A time-resolved emission technique was used to determine the quenching rate of the RO-* of 1N4S in ice samples doped with several different acids: three strong acids, HCl (pKa ) -7), HBr (pKa ) -9) and CF3SO3H (pKa ) -15) and four weak acids: HCOOH (pKa ) 3.75), HF (pKa ) 3.2), ClCH2COOH (pKa ) 2.9) and H3PO4 (pKa ) 2.2). We found that strong acids in the liquid state are also strong acids in ice, and weak acids in the liquid phase are also weak acids in ice. The experimental data indicate that the dissociation constant of HF is slightly larger than that of ClCH2OOH or H3PO4 in ice. This observation may explain the excessive use of HF in conductance experiments in ice, which were published in the literature.31 Another goal is to test the observation based on the electrical properties of HCl- and HF-doped ice that HF, a weak acid in the liquid phase, is a stronger acid in ice, whereas HCl, a strong acid in water, is a weak acid in ice. In an introductory lecture opening the 1973 ice conference in Ottawa, Onsager raised the question whether HF would be a weaker or a stronger acid in ice.15 Experimental Section We used the time-correlated single-photon counting (TCSPC) technique to measure the time-resolved emission of 1N4S. For sample excitations we used a cavity dumped Ti:Sapphire femtosecond laser, Mira, Coherent, which provided short, 150 fs, pulses. The laser’s third harmonics (THG), operating over the spectral range of 260-285 nm, was used to excite the photoacid ice samples. The cavity dumper operated with a relatively low repetition rate of 500 kHz. The TCSPC detection system was based on a Hamamatsu 3809U photomultiplier and Edinburgh Instruments TCC 900 computer module for TCSPC. The overall instrumental response was about 35 ps (fwhm). The excitation pulse energy was reduced to about 10 pJ by neutral density filters. 1N4S was purchased from TCI. HCl (1 N), HBr, CF3SO3H, HF and ClCH2COOH were purchased from Aldrich. HCOOH

J. Phys. Chem. C, Vol. 113, No. 17, 2009 7343 SCHEME 1

and H3PO4 were purchased from Merck (Germany). For transient measurements the sample concentrations were between 2 × 10-4 and 2 × 10-5 M. HPLC-grade water (Aldrich) had a resistance of >10 MΩ. Methanol of analytical grade was purchased from Fluka. All chemicals were used without further purification. The samples’ pHs in the liquid state were measured by a pH meter (Orion). The temperature of the irradiated sample was controlled by placing the sample in a (home-built) liquid N2 cryostat with a thermal stability of approximately (1.5 K. Reversible and Irreversible Photoprotolytic Cycle of Photoacids. In the present article we use a specific photoacid (1N4S) to monitor the proton concentration in ice. The photoacid fluorescence decay is sensitive to proton concentration. 1-Naphthol and its derivatives are known to exhibit large fluorescence quenching of the deprotonated form, RO-, in acidic aqueous solutions. Scheme 1 describes the photoprotolytic cycle, including proton quenching as well. Excitation of a solution at pH values lower than the ground-state pKa of photoacids in general and of 1-naphthol derivatives in particular generates a vibrationally relaxed, electronically excited ROH molecule (denoted by ROH*) that initiated a photoprotolytic cycle (Scheme 1). Proton dissociation, with an intrinsic rate constant kPT, leads to formation of the contact ion pair R*O- · · · H+, whereas reversible (adiabatic) recombination with a rate constant ka may reform the excited acid, ROH*. In general, back protonation may also proceed by an irreversible (nonadiabatic) pathway, involving fluorescence quenching of the RO-* by a proton with a rate constant kq forming the ground-state ROH. Separation of an anion pair from the contact radius, a, to infinity is described by the transient numerical solution of the Debye-Smoluchowski equation (DSE).21 In addition, one should consider the fluorescence lifetimes of all excited species, 1/k0 ) τ0 for the acid, and 1/k′0 ) τ′0 for the base. Usually, k′0 and k0 are much slower than the proton reactions and the diffusion process. The addition of excess protons to a 1N4S sample enhances the quenching rate. This process is used in the present study to monitor the proton concentration in ice of samples containing several strong and weak acids. The fluorescence quenching reaction of the RO-* form with an excess proton to form the ground-state ROH is usually described by the irreversible Smoluchowski model. This formalism is briefly described in the Discussion section. Ice Sample Preparation. Ice samples were prepared by first placing the cryogenic sample cell for about 20 min at a supercooled liquid temperature of about 260 K. The second step involved a relatively rapid cooling (5 min) to a temperature of about 235 K. Subsequently, the sample froze within a few minutes. To ensure ice equilibration prior to the time-resolved measurements, the sample temperature was kept for another 10 min at about 235 K. All samples contained 0.1% mole ratio of methanol to prevent 1N4S from aggregating at the grain boundaries of the polycrystalline ice samples.26,27 Results Figure 1a shows the time-resolved emission of the ROH form of 1N4S measured at 360 nm in liquid and in ice at four temperatures. Each panel shows four decay curves: an acid-

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Figure 1. Time-resolved emission of 1N4S measured in liquid and in ice at four different temperatures. Each panel shows an acid free, and a 4 mM concentration of the weak acids HCOOH, ClCH2COOH and HF. (a) The ROH* form measured at 360 nm. (b) The RO-* form measured at 450 nm.

Classification of Acids and Acidities in Ih Ice free (neutral pH) solution, and three solutions of 4 mM of HCOOH, ClCH2COOH, and HF. The three acids are considered weak in the liquid phase with pKa’s of 2.9, 3.2 and 3.75 for ClCH2COOH, HF and HCOOH, respectively. For each temperature the signals are almost identical at short times. At long times, however, the amplitude and decay times depend on the acid. The short-time decay rate signifies the proton transfer rate, i.e., kPT

ROH* 98 RO-* + H+

Previous studies have shown that in ice the proton transfer rate constant, kPT, is smaller than in the liquid state, and its temperature, dependence is larger in ice than in water. The activation energy in ice is ∼50 kJ/mol.37,38 The rate constant of proton transfer in liquid at 291 K is ∼3 × 1010 s-1, however, in ice at 268 K it is ∼1010 s-1, and at 237 K kPT it is ∼109 s-1. The long-time fluorescence tail depends on the reversible and irreversible recombination process, and on the overlap between the ROH* and the RO-* emission bands. Scheme 1 provides an illustration of the complexity of the process. In general, in this study the data analysis is preformed on the emission signals of the RO-* form, providing more direct and exact information on the proton concentration of acid-doped ice samples. Figure 1b shows the time-resolved emission of the RO-* form of 1N4S measured at 450 nm in the four samples mentioned above. The radiative rate constant of the neutral pH solution in the liquid state is small, hence, the long radiative lifetime, τf ≈ 16 ns at 291 K. For the neutral pH sample at short times, the signal decay rate is faster because the irreversible proton geminate recombination, which follows the initial proton transfer process, decreases the excited population of the RO-* forms. At long times, the fluorescence quenching of the RO-* form by the geminate proton is small, and consequently the decay is exponential with τ ) 16 ns. The decay rate of the acidic samples is faster than that of the sample with the neutral pH. The acidic samples of HCOOH, ClCH2COOH and HF contain the same concentration of 4 mM. In the liquid phase, the decay rate of ClCH2COOH is somewhat larger than that of HF, whereas the rate of the HCOOH sample is slower. At a concentration of 4 mM the proton concentration of HF (pKa ) 3.2) and of ClCH2COOH (pKa ) 2.9) is [H+] = 1.5 × 10-3 M and 2.0 × 10-3 M, respectively. According to scheme 1, it is therefore expected that the decay rate of the RO-* will be larger for the ClCH2COOH sample than for the HF sample. In the ice phase, the decay rate of the acidic samples is larger than in the liquid phase. The explanation we provided for this phenomenon26,27 is that there is a large proton diffusion constant in ice where, according to our explanation DH+ ≈ 10-3 cm2/s, a value 10 times larger than that of water at room temperature. For a nearly diffusion-controlled process, the pseudo-first-order reaction rate constant is kD · cH+, where kD is the diffusion-controlled rate constant and cH+ is the proton concentration. Surprisingly, in ice we found that the fluorescence decay rate of the HF sample is larger than that of ClCH2COOH. A plausible explanation for this observation is that HF and H2O are isoelectronic, and Freplaces oxygen in the hexagonal ice structure.4 This leads to a larger acidity of HF in ice than in the other weak acids that were tested (we will discuss this issue in further detail in the Discussion section). An alternative explanation is that the ClCH2COOH molecule is large, thus creating a large defect zone in the ice structure. As a consequence the effective proton diffusion constant DH+ decreases.

J. Phys. Chem. C, Vol. 113, No. 17, 2009 7345 Figure 2a shows the time-resolved emission of the ROH form of 1N4S measured at 360 nm in several strong acid samples at four temperatures in both liquid and ice phases. Strong acid HCl (pKa ) -7) and HBr (pKa ) -9) samples contained 4 mM of acid whereas for the CF3SO3H (pKa ) -15) sample it contained 2.5 mM. For comparison, the figure also shows the signals of a neutral pH sample and a weak HF acid sample. The ROH* signals of the strong acids are similar to those of the weak acids shown in Figure 1a. The short-time decay is independent of the acid. The long-time fluorescence tail’s dependence on the acid is complex, since it depends on both the reversible and irreversible proton recombination rates, as well as on the overlap between the ROH* and the RO-* bands. In general, in the liquid state the long-time fluorescence tail is almost independent of the type of acid, whereas in the ice phase the amplitude and the lifetime show a dependence on the acid. For the neutral pH and HF samples the amplitude and the average lifetime are large. Figure 2b shows the time-resolved emission of the RO-* form of 1N4S from the same samples as shown in Figure 2a, but measured at 450 nm. The decay rate of the RO-* emission depends on the nature of the acid. The decay rate of HF is significantly smaller than that of the strong acids HBr, HCl and CF3SO3H in both liquid and in ice. The decay rate of the RO-* form of 1N4S in the 4 mM HCl and HBr ice samples is almost identical. The decay rate of CF3SO3H is smaller, but its concentration is only 2.5 mM. As expected from our previous studies, the fluorescence decay rate of the acidic samples in liquid water is much smaller than in ice. Our explanation for this observation is that there is a large difference between the values of DH+ in liquid and in ice, since DH+ in ice is 10 times larger than in the liquid state. Figure 3a shows on a semilogarithmic scale the time-resolved emission of the ROH* form of 1N4S in solutions of different compositions of HF and KF at several temperatures in liquid and in ice. KF is the salt made of the acid’s conjugate base. There are five samples in each frame: neutral pH, 4 mM of HF, 4 mM of KF, and samples that contain 4 mM of HF and 1 mM of KF and 4 mM of HF and 4 mM of KF. The signals of the liquid samples at 291 K both at short and long times are almost insensitive to the HF and KF concentrations. In the solid state, the short- and the long-time components depend on both HF and KF. Figure 3b shows on a linear plot and at a short-time window the first 1.5 ns of the ROH* decay of the samples of Figure 3a. In the ice phase, the fastest decay rate of the short-time component of the ROH* form is attributed to a sample that contains 4 mM of KF. In previous studies on the photophysics and photochemistry of reversible photoacids in ice in the presence of KF, we found a similar effect. In an ice sample which contains F- ions, the ROH* decay rate of 8-hydroxy1,3,6-pyrenetrisulfonate (HPTS) or 2-naphthol-6,8-disulfonate26 is larger than for pure ice samples. Our explanation was that the immobile F- anion in ice is able to create mobile L-defects. L-defect mobility is known to be large,4 and its temperature dependence is small at temperatures above 220 K. The mobile L-defect may react with an acidic group such as an excited ROH* and remove a proton: L- + ROH* f RO-* + LH. Thus, the reaction with an L-defect increases the decay rate of the ROH* form of the photoacid in ice. In the current study we observed the same result for the 1N4S photoacid. Figure 4 shows the time-resolved emission of the RO-* of 1N4S measured at 450 nm in several samples already shown on Figure 3. The decay rate of the RO-* form in the liquid


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Figure 2. Time-resolved emission of 1N4S at 4 mM of HCl and HBr, and 2.5 mM of CF3SO3H, at four temperatures. a. The ROH* form measured at 360 nm. b. The RO-* form measured at 450 nm.

phase depends on both HF and KF concentrations. In the neutral pH solution, as well as in a solution with 4 mM of KF the fluorescence decay rates are small and almost identical. The decay rates of the RO-* sample in liquid water containing 4 mM of HF and of the sample containing 1 mM of KF (in addition to HF) are identical and are also the largest. The decay

rate of a sample that contains 4 mM of HF and 4 mM of KF is placed between the two “extreme” cases. The decay rate of the RO-* depends on both the radiative rate and the irreversible proton recombination to reform the ground-state ROH. For a further evaluation of the proton concentration and of the acidity of weak acid in ice, we used the acid-buffer concept.

Classification of Acids and Acidities in Ih Ice

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Figure 3. Time-resolved emission of the ROH* form of 1N4S at different solutions containing HF and KF salt at several temperatures. a. Semilog plot. b. Linear plot stretched to display the short-time.

HF in water is a weak acid (pKa ) 3.2); therefore, at an acid concentration of 4 mM the proton concentration is only ∼1.5 mM. At this concentration the system is very sensitive to an addition of the conjugate base, F-, as by adding KF to the solution. The addition of KF decreases the proton concentration in the solution, hence the slower decay rate in the presence of

4 mM of KF. In ice, the decay rate of the RO-* form of 1N4S in the presence of 4 mM of HF is much larger than in the liquid state, because the diffusion-controlled rate increases nearly 10ice is 10 times larger in ice. The degree of fold since DH+ dissociation of HF in ice to form H+ is similar to that of water. The decay rate of RO-* samples containing 4 mM of HF and


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Figure 4. Time-resolved emission of the RO-* of 1N4S at different solutions containing HF and the KF salt at several temperatures.

Figure 5. Time-resolved emission of the ROH* form of 1N4S at different solutions of HCl and a salt of its conjugate base, KCl, at four different temperatures.

only 1 mM of KF is distinctively smaller than that of the 4 mM HF sample. The decay rate of an ice sample that contains 4 mM of HF and KF is rather small and almost equals that of a “pure” neutral pH sample. The decay of RO-* in an ice sample that contains 4 mM of KF is identical to that of the neutral pH sample. In the Discussion section, we will further discuss the buffer effect and how it can be used to determine the pKaice of HF.

Figure 5 shows the time-resolved emission of the ROH* form of 1N4S in liquid and in ice of three different samples at four different temperatures. One sample is at neutral pH and two of the samples contain the strong mineral acid, HCl (pKa ) -7), where one of the acidic samples also contains 4 mM of KCl. The short-time component indicates that the proton transfer rate is affected neither by the presence of HCl nor the KCl salt. The amplitude of the long-time fluorescence tail and the decay



Figure 6. Time-resolved emission of the RO-* form of 1N4S at different solutions of HCl and a salt of its conjugate base, KCl, at four different temperatures.

time depend on whether the acid is present. In both acidic samples the signal decay profile is the same. The shorter decay time in samples containing 4 mM of HCl arises from the irreversible proton recombination process that decreases the population of the excited RO-*. Figure 6 shows the time-resolved emission of the RO-* form of 1N4S of the same samples as shown in Figure 5. In the liquid state, the fluorescence decay rate of the acidic samples is moderate, whereas in the ice samples the decay rate is large because the proton diffusion constant in ice is 10 times larger than in liquid water. The addition of 4 mM of KCl, a salt with the weak conjugate base Cl-, only slightly decreases the large decay rate of the RO-* in ice in the presence of a strong acid such as HCl. The small decrease in the RO-* rate in the presence of 4 mM of HCl and of KCl is attributed to the kinetic salt effect and to a small reduction of DH+. The additional ions, introduced by adding KCl into the solution, form an ionic atmosphere surrounding the charged photoacid. This atmosphere in turn partially screens the Coulomb attraction between H+ and RO-*, ultimately reducing the effective quenching rate. Moreover, ions, especially cations, tend to form a solvation shell. Consequently, the hexagonal ice structure that provides excess mobility to the proton is ruptured by ions and impurities, thus causing the proton diffusion constant to decrease. The important point to stress here is that the fluorescence decay curve of the RO-* in the presence of the strong acid, HCl, behaves differently than in the presence of a weak acid like HF. Adding a weak conjugate base (Cl-) to a strong acid (HCl) does not affect the proton concentration, hence the much smaller change in the decay rate of RO-* in the case of HCl. In contrast, in weak acid (HF) solutions, addition of a relatively strong conjugate base (F-) strongly decreases the decay rate of RO-*, which is an indication (as expected from a weak acid) for a large reduction in the proton concentration (see Figure 4).

Discussion In the current study we qualitatively classify the acidity of acids in ice Ih. We were motivated by examining the impression held by the ice research community that HF is a strong acid in ice, whereas HCl is rather weak. In general, electrical conductivity measurements in the late fifties and early sixties of the 20th century indicated that HCl, an undoubtedly strong acid in water, has a conductance behavior in ice similar to that of HF, a weak acid in water. Although water is an excellent solvent for hydrogen bonding, polar and ionic substances, almost all of them are only partially soluble in ice, and when present they are incorporated as inclusions or clusters.4 The electrical properties of ice are, however, very sensitive to small concentrations of certain impurities that can be incorporated in the hydrogen-bonded network to generate protonic point defects. The early electrical conductivity experiments of Steinemann,31 Jaccard39 and Gra¨nicher40 were performed on HF-doped ice. These pioneering electrical studies favored HF as an acid that fits the ice structure well because F- may replace the oxygen of a water molecule in the hexagonal structure and also because HF and H2O are isoelectronic molecules. Later on, the experiments of Gross et al.41 and Takei and Maeno42,43 showed that HCl behaves similarly to HF. It was concluded that at high temperatures, the L-defects are fully dissociated, whereas HCl ionized as a weak acid. At low temperatures, the static and high frequency conductivities σs and σ∞ of the HCl-doped ice samples are less well separated than for HF, and Takei and Maeno42,43 conclude that the L-defects are being trapped either at some state of the Cl- site or elsewhere.4 For the purpose of making such a classification we used several acids which are known to be either weak or strong in aqueous solutions. In the present study we used the fluorescence decay rate of the RO-* form of 1N4S to measure


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the proton concentration in acid-doped ice by the irreversible reaction

of weak acids suitable for buffers, the following equation is often written in logarithmic form:

k

pH ) pKa + log

RO-* + H+ 98 ROH

The fluorescence quenching rate depends on the proton concentration via the pseudo-first-order rate constant, k · cH+, where k denotes the overall second-order quenching rate constant and cH+ the proton concentration in the bulk ice. The Lowry-Brønsted definition of an acid suggests that a strong acid has a strong tendency to transfer a proton to another molecule, and that a strong base has a large affinity for protons. An acid’s strength is usually measured by the degree to which reactants are converted to products in a reaction such as eqs 1a and 1b:

HA + H2O a H2O+ + A-

(1a)

acid 1 + base 2 a acid 2 + base 1

(1b)

However, further examination shows that the extent to which this reaction proceeds in the direction of the products is governed not only by the tendency of acid 1 to lose a proton, but also by the tendency of base 2 to accept the proton. If the degree of proton transfer depends on the properties of both acid 1 and base 2, it is clear that the only valid way we can compare the strengths of individual acids is by measuring their tendencies to transfer a proton to the same base, which is generally chosen to be water. By testing the ability of various acids to transfer protons to water, we can rank them in order of their acid strengths. The quantitative measure of an acid’s strength is the acid dissociation constant, Ka, which is the equilibrium constant for the reaction.

[conjugate base] [weak acid]

(3)

In the biological literature this is called the HendersonHasselbalch equation. Figure 4 shows that addition of KF to HF-doped ice samples decreases the proton concentration, as predicted by eq 3. For a strong acid such as HCl, this phenomenon does not occur, and the proton concentration in ice is nearly independent of the Clconcentration. As seen in Figure 6, the quenching rate of RO-* of 1N4S only weakly depends on the KCl concentration. We found that the time-resolved emission results in Figures 1-6 clearly indicate that the acidity scale of acids in liquid water also qualitatively holds for polycrystalline ice Ih in the temperature range of 235-270 K. Data Analysis. We analyzed the time-resolved emission of RO-* of 1N4S in acidic solutions of seven strong and weak acids in liquid and in ice using the Debye-Smoluchowski formalism. The Smoluchowski model is used to describe the diffusionassisted irreversible reaction A + B f AB, where the concentration of B is in a great excess over A. In this study it is used to fit the time-resolved emission decay of the base form, RO-*, of 1N4S (the A particle) in the presence of excess protons in the ice sample (the B particle) to form the ground-state ROH (AB). We assumed that the excess proton transport toward the RO-* is the rate-limiting step. The mathematical and computational details of the Smoluchowski model are given elsewhere.44 According to the Smoluchowski model the survival probability of a single (static) donor, i.e., an excited RO-* molecule due to its irreversible reaction with a c ) [H+] concentration of protons is given by45-47 t

[H3O+][A-] Ka ) [HA]

S(t) ) exp(-c

(2)

In the current study we used acid-doped ice samples for the purpose of acid strength classification by applying the same strategy of ordering the acids by strength that is used in the liquid phase. We measured the proton concentration in ice samples doped with several weak and strong acids, whose concentrations are known. The proton concentration was estimated from the quenching rate of the reaction of the RO-* of 1N4S with the protons in the acidic ice sample. The proton quenching rate of the fluorescence of the RO-* form of 1N4S is given by a pseudo first-order rate constant. Given a known value of the rate constant (see eq 6), measuring the quenching rate provides a direct indication for the proton concentration in the ice sample. Another test for the degree of acidity of an acid is the ability of a weak acid and its conjugate base to form a buffer solution. Buffer solutions are very important for controlling pH in chemical and biological systems. This is because many simple chemicals and almost all biological molecules are weak acids. The chemical reactions that these substances carry are greatly affected by the pH of their solutions, so the control of this pH is essential. Since it is common to speak of pH instead of [H3O+], the equilibrium constant expression for the dissociation

∫ k(t′)dt′)

(4)

0

where k(t) is the time-dependent rate coefficient for the donor-acceptor pair

k(t) ) ka (a, t)

(5)

whose intrinsic proton-recombination rate constant at the reaction sphere with a radius a is ka. The pair (RO-/H+) density distribution, p(r,t), is governed by a three-dimensional Smoluchowski equation (diffusion in a potential U(r)).48 When U(r) ) 0 (no potential), eqs 4 and 5 are analytically solvable for k(t).46 Szabo47 found an approximate expression for the timedependent rate constant for the instances when U(r) * 0. When a potential is introduced, it behaves properly at both t ) 0 and t ) ∞, i.e.,

k(0) ) ka e-βU(a) and k(∞) ) [k(0)-1 + kD-1]-1 (6) where

kD ) 4πDae

(7)



is the diffusion-controlled rate constant, β ) 1/kBT and ae is an effective radius depending on the Coulombic pair attraction potential. U(a) and ae depend on the dielectric constant21 with

ae ) RD /(1 - exp(-RD /a))

(8)

and

RD )

ze2 εskBT

(9)

where a is the actual encounter radius of the specific reaction. a ) 7 Å is a commonly used value for a proton reaction in aqueous solutions.49 RD is the Debye radius, z is the molecular charge in electronic units and e is the electronic charge. The value of ae for 1N4S in its RO-* form in water with a dielelectric constant of εs)78 is 16Å. In ice, where we assume that εs ) 100, it is 12.5 Å. The nonexponentiality in S(t) is a result of a time-dependent rate constant, k(t), as depicted by the ratio k(0)/k(∞) ) 1+k(0)/ kD. In a recent study we used two 1-naphthol derivatives the 1N4S and 1N3S as probe molecules for the determination of the proton diffusion constant in ice Ih.28 Excited 1-naphthol and its derivatives are strong photoacids, pKa* ≈ 0. In the case of 1-naphthols, the proton recombination process is subdivided into two processes. The first one is a reversible (adiabatic) process to reform the excited-state ROH*, which may subsequently undergo a second photoprotolytic cycle. The second one is an irreversible (nonadiabatic) reaction of the proton with the RO-* to create a ground-state ROH. This reaction leads to the fluorescence quenching of the RO-*, and the end result is an increase at short times of the decay rate of the RO-* fluorescence. When excess protons are introduced to the sample, the long-time RO-* decay rate is much larger and depends on the excess proton concentration. In a neutral pH sample the geminate proton also quenches the RO-* fluorescence and affects the short-time decay rate. This effect is minor at long times, and thus in the data analysis we neglect this small perturbation. Strong and Weak Acid Classification in Ice Ih. In the current study we found that weak acids with a pKa in the range of 2.0-3.75 in liquid water show that their degree of dissociation in ice samples with an acid concentration of 4 mM does not exactly correlate with their pKa value in liquid water. HCOOH (formic acid) with a pKa of ∼3.75 in water exhibits the smallest acid effect on the time-resolved emission of the RO-* form of 1N4S in both liquid and ice, whereas HF with a pKa of ∼3.2 shows the largest quenching rate of the RO-* fluorescence in ice but in the liquid phase its quenching rate is between HCOOH and ClCH2COOH (see Figure 1b). Thus, there is a slight change in the acidity scale for HF in ice. This change in acidity can be seen when comparing the decay rate of 1N4S RO-* form in ice doped with HF (pKa ) 3.2) and ClCH2COOH (pKa ) 2.9) or H3PO4 (pKa ) 2.2). In liquid water, we indeed find a larger quenching rate of RO-* in the ClCH2COOH or H3PO4 samples than in the HF sample. This situation reverses in ice, where the quenching-rate of the RO-* in HF is larger than in ClCH2COOH or H3PO4, indicating a larger proton concentration, or a larger proton diffusion constant for DH+ in HF-doped ice. In our current experiment we used fitting parameters that were also used in our previous experiment.28 Below we will shortly list our assumptions and values of the parameters that are

relevant for our current experiment. The long-time asymptotic expression for the irreversible rate constant takes into account both the diffusion-controlled rate constant, kD, and the intrinsic rate constant, k(0), k(∞) ) [k(0)-1 + kD-1]-1 (see eq 6). From the time-resolved measurements of 1N4S both in liquid and ice, the intrinsic quenching-rate constant k(0), (eq 6), in ice at 260 K is about 5 × 1011 M-1 s-1. For a diffusion constant of 10-3 cm2 s-1 in ice and for a large dielectric constant (ε ) 100), the second-order diffusion-controlled rate is also 5 × 1011 M-1 s-1. Thus, the overall rate constant, k(∞), is half of the values of both k(0) and kD. A diffusion constant with a value of 10-3 cm2 s-1 was used in the analysis of all the various acid ice samples used in this study. We used the proton concentration as the only adjustable parameter in the fitting of the time-resolved emission of the RO-* form of 1N4S. The strong acids show that in aciddoped ice, with a proton concentration of 4 mM (i.e., cH+ ) cacid) and with the above-mentioned value for the proton diffusion constant, the data fit is rather good in the temperature range of 242-263 K. As expected from eq 2 we generally found that for the three strong acids (HCl, HBr and CF3SO3H), the acid concentration and the proton concentration are the same within an experimental error of (10%. For the weak acids, the actual proton concentration is somewhat smaller than the calculated concentration according to their pKa value in water at room temperature. Figure 7a shows the 1N4S decay in various HCl concentrations in the range of 1-10 mM at four temperatures in water and in ice. Figure 7b shows the decay of RO-* of 1N4S in HF-doped ice in various concentrations and at four temperatures. The measurement of the decay rate of the time-resolved emission of the RO-* is proportional to K(∞) · cH+, where k(∞) (eq 6) is independent of the kind of acid, although it does depend on both kD and k(0). Knowing the value of DH+ in water (DH+ = 9 × 10-5 cm2 s-1) provides the value of kD in water. From the best fit to the time-resolved emission of the RO-* we found a value of 5 × 1010 M-1 s-1 for k(0). In our previous studies26-28 we found that DH+ in ice is 10 times larger than that of liquid water, thus kD is also 10 times larger (eq 7). The intrinsic decay rate, k(0), in ice is larger than that in liquid water. From the best fit of the RO-* decay we find that k(0) is also 10 times larger, which means that its value in ice is 5 × 1011 M-1 s-1. The HCl-doped ice results show that k(∞) is nearly independent of the temperature in the relatively narrow temperature range of 243-263 K, and that at T ) 258 K it yields a maximum value of 3 × 1011 M-1 s-1.28 Furthermore, k(∞) is independent of the acid concentration in the range of 1.0-10 mM, which is an expected behavior from a strong acid. In HF-doped ice the situation is different: k(∞) · (cH+/cacid) varies with the acid concentration. The dependence of the cH+/cacid ratio on cacid indicates that at low HF concentrations the degree of dissociation is slightly larger than at high HF concentrations and this is, of course, in accord with what is expected from a weak acid (see Figure 8). Therefore, it can be said that in principle, pKaHF in ice can be calculated from cH+ extracted from the decay rate pattern of the RO-* of 1N4S. Figure 8a shows on a log-log plot the dissociation curves of weak and strong acids, calculated according to eq 2 for pKa values of 3.5, 3.2, 2.0, and -1.0. As seen in the figure, for weak acids (pKa > 2), the proton concentration is smaller than the acid concentration at cacid > 5 × 10-4 M. The extent of the acid dissociation decreases as the acid concentration increases. For strong acids (pKa < -1), the acid and proton concentrations are nearly the same (a constant slope in the figure). The degree of dissociation of strong acids is large and close to unity at low


Uritski et al.

Figure 7. Time-resolved emission of 1N4S with strong acids (HCl) and weak acid (HF) in the concentration range of 1-10 mM, at four different temperatures. a. HCl. b. HF.

and medium acid concentrations. We will examine our experimental results for HCl and HF. As aforementioned, HCl is a strong acid in aqueous solutions with a pKa of -7, and HF is a weak acid with a pKa of 3.2. The decay constant of the RO-* form of 1N4S is used as an index for the acid concentration in ice, making it a kind of a nanoscopic pH meter. Figure 8b shows on a reduced concentration range the dissociation curves of Figure 8a as well as the actual proton concentrations of HFdoped ice samples, as monitored by the fluorescence quenching of 1N4S in the range of 1-10 mM. The fit to the calculated plot indicates that pKaHF in ice is very close to its value in water.

The best fit is achieved when the value of pKaHF is close to 3.6. This fit has a margin of error of ∆pKa ) ( 0.4. We argued at the beginning of the discussion that the pKa of a weak acid in water can also be measured using the Henderson-Hasselbalch equation (eq 3), whereby an acidic solution is treated with a salt containing the acid’s conjugate base, and in our case, HF and KF. Thus the pH could be set at a fixed value, and acidic or basic impurities in the solution could be neutralized within the so-called buffer capacity. According to eq 3, when [KF] ) [HF], the pH equals the pKa, and thus the pKa of the acid could be determined. The experimental


J. Phys. Chem. C, Vol. 113, No. 17, 2009 7353 significant in creating L-defects, as opposed to Cl- ions, which do not produce a large quantity of L-defects, and then the kind of acid in use is important. Our results on the acidity classification in ice nicely fit the results by Minot and co-workers,33 who studied periodic DFT calculations on the ice system interacting with HCl and HF. In their model, HX substitutes a water molecule in the cubic ice matrix. Their study took into account thermodynamics considerations. Energetic barriers can prevent penetration of HX into the ice crystal structure. According to their calculations, HCl inside the ice bulk structure completely dissociated. Moreover, a hydrogen transfer to a second molecule takes place, resulting in a separate ion pair. On the other hand, HF does not show ionization and remains in its molecular form. The different behaviors of HCl and HF inside the ice can be attributed to the different electron affinities. Minot et al.33 reproduced the experimental observations of HCl and HF as strong and weak acids in liquid water, respectively. In an interesting recent study, Ayotte and co-workers50 investigated cryogenic mixtures of water and HF in order to explore the spectral signature of the transient structures that are involved in the process of ionization of HF molecules in aqueous solutions, which ultimately lead to the creation of proton-shared intermediates and of contact ion pairs:

[H2O · HF] T [H2O · H+ · F-] T [H2OH+ · F-]

(10)

Dilute cryogenic solutions of HF in H2O were recently shown51 to display the spectral signature of aqueous protons, similarly to the behavior observed for the strong acids HCl and HBr, suggesting a similarly extensive degree of ionization at 40 K in amorphous solid water. Figure 8. Log-log plot of the dissociation curve of weak and strong acids, calculated according to eq 2 for different pKa values (3.6, 3.2, 2.0, -1.0). (a) Extended scale. (b) Reduced scale (including experimental HF data).

results shown in Figure 4, in which 4 mM of KF were added to 4 mM of HF, allowed us to calculate the proton concentration from the decay rate of the RO-* of 1N4S. We found that [H+] ) 2.0 × 10-4 M, which corresponds to a pKa value of 3.6. Accordingly, this result is similar to the one yielded from the weak acid dissociation plot in Figure 8b (pKa ) 3.6). In conclusion, weak acids with pKa values of around 3 dissociate in ice, at low concentrations of roughly 1 mM with a reasonable degree of dissociation. Weak acids’ degrees of dissociation are about 30%, while those of strong acids at 1 mM reach 100%. The difference in the proton concentration in ice between a weak acid, such as HF, and a strong acid, such as HCl, at a concentration range of millimolars, is not measured in orders of magnitude but by a mere factor of 3. Conductivity measurements at low acid concentrations of 10-4 M, such as those performed in the far past and those that were performed later on by Takei and Maeno42,43 in the 1980s and 1990s, will not yield large differences between the results of the two types of acids, on condition that the proton concentration is mainly responsible for the ice conductivity. It may be that the historical debate regarding the preferential use of HF over a strong acid, such as HCl or HBr, in ice is irrelevant to our current results in the relatively high acid concentration range of 1-10 mM. The proton concentration at a low concentration of HF and HCl as a source of doping is of no real importance, and the conductivity experiments should show similar results to ours. Conversely, it may be that F- is

Summary We studied the fluorescence quenching of the RO-* of 1N4S in liquid water and in ice in the presence of small concentrations of strong and weak acids. We used a time-resolved emission technique to monitor the fluorescence quenching by excess protons in both liquid water and in ice. In general, we found that the proton quenching rate of 1N4S in ice depends on both the acid concentration and the strength of the acid. From the data analysis we concluded that strong acids release more protons in ice than weak acids. In the milimolar concentration employed in this study, the proton concentration released into the bulk ice by a weak acid is smaller by only about a factor of 3 than that for a strong acid. HF is somewhat stronger in ice than other weak acids with smaller pKa values (stronger acids in liquid than HF). These findings are in accord with the common knowledge of the ice community that it is preferred to dope ice with HF to enhance electrical conductivity. From the experimental results we estimated that the pKa value of HF in ice is very similar to its value in water. Acknowledgment. We thank Professor R. B. Whitworth for helpful discussions. This work was supported by grants from the Israel Science Foundation and from the James-Franck German-Israel Program in Laser-Matter Interaction. References and Notes (1) Fletcher N. H. The Chemical Physics of Ice; Cambridge University Press: London, 1970. (2) Hobbs. P. V. Ice Physics; Clarendon Press: Oxford, UK, 1974. (3) Physics and Chemistry of Ice, 5th ed.; Walley, E., Jones, S. J., Gold, L. W., Eds.; Royal Society of Canada: Ottawa, 1973.

7354 J. Phys. Chem. C, Vol. 113, No. 17, 2009 (4) Petrenko, V. F.; Whitworth, R. W. The Physics of Ice; Oxford University, Press: Oxford, UK., 1999. (5) Bolton, K.; Pettersson, J. B. C. J. Am. Chem. Soc. 2001, 123, 7360. (6) Jaccard, C. Ann.New York Acad. Sci. 1965, 125, 390. (7) Bjerrum, N. Science 1952, 115, 385. (8) Kobayashi, C.; Saito, S.; Ohmine, I. J. Chem. Phys. 2001, 115, 4742. (9) Podeszwa, R.; Buch, V. Phys. ReV. Lett. 1999, 83, 4570. (10) (a) Eigen, M. Proton Transfer. Angew. Chem., Int. Ed. Engl. 1964, 3, 1. (b) Eigen, M.; Kruse, W.; Maass, G.; De Maeyer, L. Prog. React. Kinet. 1964, 2, 285. (11) Eigen M.; de Maeyer L. The Structure of Electrolytic Solutions; Wiley: New York, 1959; p 64. and following. (12) Kelly, I. J.; Salomon, R. R. J. Phys. Chem. 1969, 50, 75. (13) Camplin, G. C.; Glen, J. W. Physics and Chemistry of Ice, 5th ed.; Walley, E.,; Jones, S. J., Gold, L. W., Eds.; Royal Society of Canada: Ottawa, 1973; p 256. (14) Kunst, M.; Warman, J. M. J. Phys. Chem. 1983, 87, 4093. (15) Engelhardt, H. Physics and Chemistry of Ice, 5th ed.; Walley, E., Jones, S. J., Gold, L. W.; Royal Society of Canada: Ottawa, 1973; p 226. (16) Ireland, J. E.; Wyatt, P. A. AdV. Phys. Org. Chem. 1976, 12, 131. (17) (a) Gutman, M.; Nachliel, E. Biochem. Biophys. Acta 1990, 391, 1015. (b) Pines, E.; Huppert, D. J. Phys. Chem. 1983, 87, 4471. (18) Tolbert, L. M.; Solntsev, K. M. Acc. Chem. Res. 2002, 35, 19. (19) (a) Rini, M.; Magnes, B. Z.; Pines, E.; Nibbering, E.T. J. Science 2003, 301, 349. (b) Mohammed, O. F.; Pines, D.; Dreyer, J.; Pines, E.; Nibbering, E. T. J. Science 2005, 310, 5745. (20) Tran-Thi, T. H.; Gustavsson, T.; Prayer, C.; Pommeret, S.; Hynes, J. T. Chem. Phys. Lett. 2000, 329, 421. (21) Agmon, N. J. Phys. Chem. A 2005, 109, 13. (22) Spry, D. B.; Fayer, M. D. J. Chem. Phys. 2008, 128, 084508. (23) Siwick, B. J.; Cox, M. J.; Bakker, H. J. J. Phys. Chem B 2008, 112, 378. (24) Buch, V.; Milet, A.; Va´cha, R.; Jungwirth, P.; Devlin, P. Proc. Natl. Acad. Sci. U.S.A. 2007, 104, 7342. (25) Mondal, S. K.; Sahu, K.; Sen, P.; Roy, D.; Ghosh, S.; Bhattacharyya, K. Chem. Phys. Lett. 2005, 412, 228. (26) Uritski, A.; Presiado, I.; Huppert, D. J. Phys. Chem. C 2008, 112, 11991.

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JP900338C

Classification of Acids and Acidities in Ih Ice - The Journal of Physical

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